Motivational Goal Bracketing - School of Economics and ...

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optimal to provide low effort from the perspective of self 1 (self 2) if and only if β p ¯y − c < 0, (3) Thus, whenever both (2) and (3) hold, the individual has a self-control problem. The following assumption summarizes this. Assumption 1 (Self-control problem) Self 0 prefers high effort in each task, but in the absence of a goal, the self making the effort decision on a task will choose low effort, i.e., p ¯y ≥ c and βsc ≡ c p ¯y > β. (4) 3 The basics of goal setting (a single task) To prepare for our main analysis, we first look at how an individual sets a goal for himself if there is only a single task to be completed. When designing his task goal, self 0 anticipates what it takes to motivate self 1 to provide effort. We therefore solve by backward induction: starting with the effort choice at date 1, we ask how self 1 responds to a given goal. Then we determine what is the optimal goal from the perspective of self 0. 3.1 The incentive effect of a given goal For a given goal related to the task, self 1 provides high effort if and only if the expected utility of self 1 if he works hard exceeds that if he shirks: U1(a; ē) ≥ U1(a; e). For a ≤ ¯y this “incentive constraint” is given by (see Appendix A.1): a β (µ − 1) [Pr(loss|e) − Pr(loss|ē)] ≥ c − β p ¯y, (5) where Pr(loss|e) gives the probability that the individual falls short of the goal (thereby suffering a psychological loss) when providing effort level e. The incentive constraint shows how and why a goal motivates an individual to work hard. Think of studying for an exam. Cramming yields self 1 net-utility β p ¯y − c, which however is negative: the benefit from an expected good grade does not compensate for the cost of studying hard, because of the individual’s present bias (Assumption 1). Hence, self 1 would refrain from working hard in the absence of a goal. Motivating himself to study for an exam however is easier if he has a target grade, as he then fears suffering a loss from not reaching his goal. If self 1 shirks, the probability of failing the goal is larger (it is equal to 1) than if he works hard (the probability then is 1 − p) – so the left-hand side of the incentive constraint is positive. Hence, with an appropriately chosen goal, the loss avoided by exerting effort offsets the net cost from hard work. More precisely, the goal level, where (5) just holds, is given by â = c − β p ¯y . (6) β p (µ − 1) 10
The more severe the present bias (i.e., the lower β), the more difficult it is to incentivize self 1 and thus the higher the required goal level â. If however the present bias is so strong that â exceeds ¯y, self-regulation becomes impossible. The reason is that in this case the incentive constraint (5) needs to be modified: with such a goal the individual experiences a loss no matter whether he works hard or shirks. As loss aversion no longer kicks in, the goal simply cancels out from the incentive constraint. 10 In sum, self-regulation with a goal is feasible if and only if â ≤ ¯y, which is equivalent to 1 µ βsc ≤ β (βsc is defined in Assumption 1). 3.2 What goal does self 0 choose? Holding the effort level e fixed, a higher goal increases the chance of falling short of the aspired outcome a. But this matters more than the chance of exceeding a, because losses loom larger than gains of equal size. So a higher goal level is painful, because it reduces the utility self 0 expects from a given effort level e: d d a U0(a; e) < 0. This shows clearly that the only purpose of setting a > 0 is to discipline self 1 to put in more effort than he would exert in the absence of a positive goal. Thus, the choice of self 0 is a relatively simple one: either avoid the pain from an ambitious goal by abstaining from goal setting, and live with low effort; or pick the goal level that just suffices to motivate self 1 to work hard (if this is feasible). In other words, self 0 will specify a positive goal if his expected utility with goal â and high effort in the future exceeds the utility from a = 0 and low effort in the future: U0(â; ē) ≥ U0(0; e) = 0. Lemma 1 below characterizes this in terms of β (it corresponds to Proposition 1 in Koch and Nafziger 2008). 4 Risk pooling vs leaning back (the no-information scenario) We start our analysis of the two-task setting with the no-information scenario, where the individual does not learn about the first task outcome before working on the second task. For example, think of studying for two exams in unrelated subjects, that take place in close sequence. Before even taking the first exam, you need to already study for the second exam. So all you know is how much (or little) effort you put into preparing for the first exam. 4.1 Self-regulation with narrow goals If the individual sets narrow goals, he will evaluate task outcomes separately. (Did I reach the target grade in the first exam? Did I in the second?) Given the symmetry of tasks, the problem for each task hence mirrors the one in the single-task setting above. The minimum 10 −β µ {p (a − ¯y) + (1 − p) a} − c ≥ −β µ a. ⇔ β p ¯y ≥ c, which does not hold because of Assumption 1. 11
Page 1 and 2: Motivational Goal Bracketing Alexan
Page 3 and 4: Bandura, for example, writes that
Page 5 and 6: introduces our model of goal settin
Page 7 and 8: outcome of the first task before wo
Page 9: In the absence of a goal, simply se
Page 13 and 14: Now consider what it takes to get b
Page 15 and 16: 4.3.2 The leaning-back effect Yet t
Page 17 and 18: task. So the fear of a loss - which
Page 19 and 20: 6 Conclusion An important reason wh
Page 21 and 22: single-task incentive constraint (5
Page 23 and 24: So the expected utility of self 0 u
Page 25 and 26: where κ ≡ 2 p−p2 +(1−p) 2 µ
Page 27 and 28: References Abeler, J., A. Falk, L.
Page 29 and 30: Herweg, F., and D. Müller (2008):

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